An electrical grid, also referred to as a power grid, is an interconnected network for delivering electricity to consumers. FIG. 1 depicts an example of an electrical grid. A grid may include generating stations that produce electricity, high-voltage transmission lines that carry electricity to demand centers, and distribution lines that connect consumer electronic devices to the grid through wall sockets or other types of electrical outlets.
A “grid” does not imply any physical layout and may refer to an entire electrical network for a given area, country, region, local transmission grid, distribution grid or the like. A so-called “smart grid” can monitor the production and distribution of electricity and uses communications technology to gather and act on analog or digital information in an automated fashion to improve the efficiency, reliability and sustainability of the grid.
Electricity can be monitored at different levels in an electrical grid. For example, a monitoring device at an electrical substation may be used to provide general information about power flow, or a household monitoring device can provide feedback about energy consumption, costs, and estimates of greenhouse gas emissions. Despite developments in monitoring technologies, the ability to effectively and reliably monitor electricity on a grid to detect events and to predict instabilities remains limited due to, for example, aging grid equipment, obsolete system layouts, cost-prohibitive monitoring equipment, insufficient sampling rates and temporal resolutions, and an inability to collect data from a critical number of geographically disparate locations on a grid.
Phasor measurement units (PMUs), also known as synchrophasors, are monitoring devices that provide synchronized measurements of real-time phasors of voltages and currents at respective locations on an electrical grid. A phasor, as defined in more detail below, is a vector representation of a waveform that is commonly used to analyze electrical waveforms carried on an electrical grid. PMUs filter incoming voltage and/or current waveforms through a low-pass filter and often apply a discrete Fourier transform (DFT) algorithm to extract the frequency and phase of the dominant, 60 Hz carrier component, prior to generating phasor measurements. This procedure may result in loss of data about distortions to the incoming waveform, which may not be able to be reconstructed. Specifically, distortions to the waveform that are not associated with the dominant carrier frequency may be lost.
Synchronization of phasor measurements is achieved by using a common time source to sample electrical waveforms at different locations. For example, data about frequency disturbances may be received at a central processing facility from PMUs at different locations on an electrical grid. This data may be used to identify information about electrical anomalies that indicate the state of an electrical grid. However, PMUs are of limited use because they are prohibitively expensive, installed sporadically only at power stations or substations of an electrical grid, and data obtained from PMUs may not include information about short transients and geographically isolated events for making reliable predictions of instabilities.
PMUs are installed at electrical substations to monitor properties, such as voltage and current, of the electricity at the substation and to report the characteristics of the properties to a central monitoring facility where the characteristics of multiple PMUs are analyzed. PMUs monitor and report electrical properties by generating sample measurements of the electrical properties, converting the sampled values into phasors, combining the phasor data with Global Positioning System (GPS) time information, and transmitting the combined data to the central monitor. GPS time information is used as a common time source to synchronize sampled values of electrical waves measured at the various substations on a grid. Phasors are complex numbers that represent a sinusoidal function with time-invariant frequency, phase, and amplitude. They are often represented as vectors on a complex plane with a given phase angle φ and amplitude. Grid instabilities may be determined based on differences between synchronized phasor components.
FIG. 2A depicts a sinusoidal waveform of electricity carried on an electrical grid. The sinusoidal waveform can be represented mathematically as:x(t)=Xm cos(ωt+φ)where Xm is an amplitude, ω is a frequency in radians per second, φ is a phase angle in radians, and t is time.
FIG. 2B depicts a phasor representation of the sinusoidal waveform of FIG. 2A. The conversion of the waveform into a phasor can be represented mathematically as:
  X  =                              X          m                          2                    ⁢              e                  j          ⁢                                          ⁢          φ                      =                            X          m                          2                    ⁢              (                              cos            ⁢                                                  ⁢            φ                    +                      j            ⁢                                                  ⁢            sin            ⁢                                                  ⁢            φ                          )            Where, Xm is the peak amplitude,
      X    m        2  is the magnitude of the phasor in R.M.S., and φ is the phase angle. Therefore, a phasor contains information only about the magnitude and phase angle of a waveform. A phasor is only accurate when the frequency of the waveform is constant. What is more, the comparison of two or more phasors assumes that the frequencies of the waveforms represented by the phasors are equivalent. Although a phasor may be converted back into the original waveform, the phasors recorded and reported by PMUs cannot be converted back into the original waveform because information is irreducibly lost during the conversion process.
A PMU measures electrical waves and outputs time-stamped voltage and current phasors based on the measurements. Phasors from different PMUs are compared to assess the static state of a grid and/or to analyze an event that has occurred. For example, a large difference between phase angles measured at different PMUs may imply static stress on a grid. Moreover, a growing phase angle difference may indicate an approaching instability. This occurs because, in general, active (real) power flow is driven by the voltage phase angle difference, called the transmission angle or load angle, between the source and destination in an AC electrical grid. Thus, the larger the phase angle difference between the source and the sink, the greater the power flow between those points. Exceeding a maximum power transfer (indicated by a maximum phase angle) may lead to power grid instability. Thus, e.g., growing phase angle differences may be recorded in the time leading up to an electrical blackout.
FIG. 3 depicts components of a conventional phasor measurement unit (PMU). Again, PMUs are installed at substations and monitor the three phases of a medium or high voltage distribution system and relay extracted phasor information to a central location at low rates (e.g., about 30 Hz). Analog inputs include voltages and currents obtained from secondary windings of the three phase voltage and current transformers located at substations. The analog inputs are processed by an anti-aliasing filter to restrict the bandwidth of a signal to remove input frequencies that are higher than the Nyquist frequency, which is the minimum sampling rate required to avoid aliasing. Often a low-pass filter is set at a low corner frequency (maybe around 200 Hz) to improve the quality and resolution of the converted phasors. This filtering may remove the impulse-like transients and high-frequency components of the original waveform.
A digital decimation filter converts the sampled data to a lower sampling rate to provide a digital antialiasing filter concatenated with the analog antialiasing filter. The analog AC waveforms are digitized by an analog to digital convertor (e.g., 16-bit A/D converter) for each phase. A phase lock oscillator along with a GPS reference source provides the needed high speed synchronized sampling with about 1 μs accuracy. The phasor microprocessor then calculates the phasor using digital signal processing techniques. A network interface can then communicate the phasor data to a central processing receiver that aggregates data from multiple PMUs.
The cost and complex installation of PMUs hinders their widespread adoption. For example, only a few PMUs are typically installed on any grid because their cost can range from $30,000 to $40,000 each. Consequently, PMUs and similar devices may provide data that is sparse and of limited use because PMUs are installed at limited preselected substations on a grid, collect data at low rates, and convert original waveforms to phasors often representing the behavior of only the carrier frequency.
The frequency monitoring network (FNET) project, developed at the University of Tennessee, Knoxville, is another system used for monitoring an electrical grid. The FNET project uses a series of low-cost, distributed devices that sample at 1.44 kHz. Similar to PMUs, the FNET devices are limited to calculating and relaying phasor information at 10 Hz.
Another monitoring device is the imc DataWorks Climate Retrieval and Observations Network of the Southeast (CRONOS) flex/C-Series that are able to capture and save multiple channels of waveform data to disk at high sampling rates with reference to a GPS clock. These devices may be combined with an external networked computer system and current clamps to measure properties of an electrical grid. However, this setup is complicated, very expensive, involves multiple vendors and hardware products, and is prone to error.
Another monitoring device includes Libelium Waspmote, which is a general purpose, microprocessor driven hardware platform for experimental applications Like the CRONOS system, these devices offer a general purpose platform that require external hardware components to measure properties of an electrical grid. Moreover, these devices sample at low rates that is insufficient for many analysis tasks that would be useful for detecting a vast array of different types of anomalies occurring on an electrical grid.
Yet another monitoring device is Power Standards Lab's PQube, which is a power quality and event monitor. This device detects events and provides a wealth of information about the events. However, installation is complex, expensive and requires a licensed electrician. Moreover, these devices are event detectors that can provide waveform information only centered on an event. These devices do not continuously capture waveform data.
Accordingly, there is a need for a compact, easy to install, high-fidelity, and low-cost monitoring device that collects data about household-level electrical waveforms. The device should be easy to operate and improve monitoring of an electrical grid by facilitating post-event analysis, adaptive protection, state estimation, and pattern recognition to detect potential events or instabilities. Effective utilization of this technology should be useful to mitigate blackouts and to learn about the real-time behavior of an electrical grid.